Seleção de modelos e estimação de parâmetros em identificação de danos estruturais via transformada integral generalizada e inferência bayesiana

Abstract

The present work addresses the inverse problem of structural damage identification in an Euler-Bernoulli beam. The mathematical model of the beam dynamics includes a cohesion field for modelling the damage field. This one is described by the sum of continuous exponential base functions and the dynamic response of the structure is obtained with the Generalized Integral Transform Technique, which provides an analytical-numerical solution. The inverse damage identification problem is formulated according to bayesian inference and divided into two steps. At a first level, the estimation of damage parameters is made for different model classes, and sampling is done using the Transitional Markov Chain Monte Carlo method (TMCMC). At a second level, it is performed the model class selection according to the models considered in the first stage. Combining these two analyses, it is possible to predict the number of damaged regions, as well as the location and shape of the damage, without the need for computational meshes on the structure. The verification of the proposed methodology is based on numerical simulations considering a simply supported Euler-Bernoulli beam and analyzing the performance of the method in three different damage scenarios under different conditions. The method was able to solve the proposed problems with a relatively low number of parameters when compared with other methods from the literature.